A Maclaurin series is a Taylor series expansion
of a function about 0,

(1)

Maclaurin series are named after the Scottish mathematician Colin Maclaurin.

The Maclaurin series of a function up to order may be found using Series[f,
x, 0, n]. The th term of a Maclaurin series of a function can be computed in the Wolfram
Language using SeriesCoefficient[f,
x, 0, n] and is given by the inverse Z-transform

(2)

Maclaurin series are a type of series expansion in which all terms are nonnegative integer powers of the variable. Other more general
types of series include the Laurent series and
the Puiseux series.